A two-wheeled self-balancing robot is considered for investigating the responses of a control moment gyroscope powered by a proportional controller to prevent the robot rollover against the constant inertia forces because of accelerations of the wheels of the robot. The amplitudes of the frequency equations related to the required angular momentum of flywheels with an optimum controller gain were also found. A simulation model of the robot using computer-aided engineering software (RecurDyn) is built to verify the equations of a Lagrangian model. The results of both obtained from the Lagrangian and that from RecurDyn simulations are analyzed comparatively, in which the proportional control loop reduces the required flywheel speeds Ω of gyros and keeps the robot in a very small amplitude of a stable sinusoidal motion in the upright position.

考虑使用两轮自平衡机器人来调查由比例控制器提供动力的控制力矩陀螺仪的响应，以防止由于机器人的车轮加速度而使机器人克服恒定的惯性力而侧倾。还发现了与具有最佳控制器增益的飞轮所需的角动量有关的频率方程的振幅。建立了使用计算机辅助工程软件（RecurDyn）的机器人仿真模型，以验证拉格朗日模型的方程。比较分析了从拉格朗日和RecurDyn仿真获得的结果，其中比例控制环降低了所需的陀螺仪飞轮速度Ω，并使机器人在直立位置处于稳定正弦运动的很小幅度。